User blog:Logo12/Number Terrain
So one day I was bored and started to play with http://prntscr.com/4n9mvb again, and eventually got to play with Sounds (http://prntscr.com/4n9ocs). That thing is a repeating pattern of the last (1s) digit of 2^n, which is known as a 2,4,8,6 pattern. I had been trying to find these repeating pattern of specific numbers since, and I've got 20 in the 10s digit, so: http://prntscr.com/4n9p14 ...40 seconds? Nah, that's too long. Let me merge them.... http://prntscr.com/4n9ply Better... but it sounds terrible. Maybe some arrangements? http://prntscr.com/4n9sap Okay, for the 100s digit.... After some investigation it loops per 100 powers (It also has glide reflection!) http://prntscr.com/4n9uq7 And the 1000s digit.... It loops for... 500? http://prntscr.com/4na0p3 Okay, it's too much, and before I have found the pattern, I've found something special about this: All digits (except the last) has an even chance to be any number. So I started to try those numbers stuffs... http://prntscr.com/4na3m8 This is the distribution of 5^n's digits in the iterations calculated above, which isn't quite clear because of lacking of number data and how MatrixPlot forces the max value to be 1 and others to be colored accordingly to the ratio of max value and the value, which I don't know if they are actually spread evenly or not (it may differ by a tiny digit) So, I decided to make my own "grid" which involves using Circles (Disks) and with the value on it, while the color would be yellow when spread evenly (1), Green when it is higher than normal (which became blue if it is 10, but it turns out better), and Red when it is lower than normal (or black if 0, just for better vision). So here is the code: GraphicsGrid[Function[e, Graphics[{ If[e 0, Black, Hue[1/6 + Log[e/6]], Disk[], Text[ StyleIf[e > 0, Black, White, FontFamily -> "Oetztype", Magnification -> If[IntegerQe, 4, 2]]]} ]], Table[BinCounts[ Table[IntegerDigits10, x1, {i, x, x - 1 + 4 5^(x - 1)}], {0, 10}]/(2 5^(-2 + x)), {x, 1, 6}], {2}], Background -> , }, ImageSize -> {500, Automatic}] Okay, this is the original code that shows the distribution thingy, which uses the Oetztype (BTD5 font) for styling. Here I have an example of 5 from 1st to 8th digit, which I stored because it took ages to finish: http://prntscr.com/4na5h8 Here's a Matrix Plot for comparison: http://prntscr.com/4na5lm (So it is apparently smaller in code size) Then, to make it easier (lazier way) to set the y (in y^n), I have made an ugly panel thing: DynamicModulePanel[Column[{ Panel[ Column[ {Style["The nth digit of " Dynamic[y^n , 30, FontFamily -> "Oetztype"], Manipulator[Dynamicy, {0, 100, 1}, Appearance -> {"Open", Large}, AppearanceElements -> {"StepLeftButton", "StepRightButton", "InputField"}, ImageSize -> Large]}, Alignment -> Center], Background -> Hue0, 0.8 ], Dynamic[ GraphicsGrid[Function[e, Graphics[{ If[e 0, Black, Hue[1/6 + Log[e/6]], Disk[], Text[StyleIf[e > 0, Black, White, FontFamily -> "Oetztype", Magnification -> If[IntegerQe, 4, 2]]]} ]], Table[ BinCounts[ Table[IntegerDigits10, x1, {i, x, x - 1 + 4 5^(x - 1)}], {0, 10}]/(2 5^(-2 + x)), {x, 1, 6}], {2}], Background -> , }, ImageSize -> {500, Automatic}] ]}, Alignment -> Center], Background -> Hue0, 0.9]] Okay, this code is around 1500 chars, which is the limit of a chat message. This is the result: http://prntscr.com/4na6f5 Looks cool enough. *UPDATE* By finding a new tool (Power Mod), the running speed is now faster and allowing me to calculate digits up to the 1000000s! So with this palette set (and a height of 67), I decided to call these number terrains. Here are some classifications: Classifications *Personal opinion Classification of First 100 Elements 0 - Sky 1 - Sky 2 - Land 3 - ImpureLand 4 - Land 5 - Underwater 6 - ImpureLand 7 - ImpureLand (Contains Red) 8 - Land 9 - ImpureLand 10 - Sky 11 - ImpureLand 12 - Land 13 - ImpureLand 14 - Land 15 - TurquoiseSea 16 - ImpureLand 17 - ImpureLand 18 - Desert 19 - ImpureLand 20 - Sky 21 - ImpureLand (Almost Pure) 22 - Land 23 - ImpureLand 24 - Land (2 Layers of Greens) 25 - Underwater 26 - Beach 27 - ImpureLand 28 - Land 29 - ImpureLand (Almost Pure) 30 - Sky 31 - ImpureLand (Almost Pure) 32 - Desert 33 - ImpureLand 34 - Land 35 - Underwater 36 - ImpureLand 37 - ImpureLand 38 - Land 39 - ImpureLand (Almost Pure) 40 - Sky 41 - ImpureLand 42 - Land 43 - ImpureLand (2 Layers of Greens) (Contains Red) 44 - Land 45 - Underwater 46 - ImpureLand 47 - ImpureLand 48 - Land 49 - ImpureLand (3 Layers of Greens) 50 - Sky 51 - ImpureLand (2 Layers of Greens) 52 - Land 53 - ImpureLand 54 - Land 55 - Underwater 56 - ImpureLand 57 - ImpureLand (3 Layers of Greens) 58 - Land 59 - ImpureLand 60 - Sky 61 - ImpureLand (Almost Pure) 62 - Land 63 - ImpureLand (2 Layers of Greens) 64 - Land 65 - ImpureSea 66 - ImpureLand 67 - ImpureLand (2 Layers of Greens) 68 - Desert (3 Layers) 69 - ImpureLand (Almost Pure) 70 - Sky 71 - ImpureLand (4 Layers of 1s, Almost Pure) 72 - Land 73 - ImpureLand 74 - Land (2 Layers of Greens) 75 - Underwater 76 - Beach 77 - ImpureLand 78 - Land 79 - ImpureLand (3 Layers of 1s, Almost Pure) 80 - Sky 81 - ImpureLand 82 - Desert 83 - ImpureLand (2 Layers of Greens) 84 - Land 85 - Underwater 86 - ImpureLand 87 - ImpureLand (2 Layers of Greens) 88 - Land 89 - ImpureLand (2 Layers of Greens) 90 - Sky 91 - ImpureLand 92 - Land 93 - ImpureLand (2 Layers of Greens) (Contains Red) 94 - Land 95 - TurquoiseSea 96 - ImpureLand 97 - ImpureLand 98 - Land 99 - ImpureLand (3 Layers of Greens) 100 - Sky Special Cases 1 - The only Sky that has the 1s digit at 1. 255 - Symmetric Turquoise Sea (Excluding the first digit) 895 - Same as 255 on the first 7 layers, the only 2^x95 that is symmetric y95 - With exception of 1,2,4,8, are all the same. 305 - Underwater without Visible Land 10005- Identical to 50005 and 90005 12735- TurquoiseSea with Blue on the 7th Row 13375- Symmetric TurquoiseSea with Blue on the 7th Row 999999 ImpureLand without Visible Land (7 Layers of Greens) 687999 ImpureLand without Visible Impurities (3 Layers of Greens, 4 Layers of 1s, Almost pure) 4765624Land without Visible Land (7 Layers of Greens) Also Symmetric. 9765624Same as above 2265624Same as above 7265624Same as above 3626068Desert without Visible Land (7 Layers of Greens) 4251068Same as above 3001068Same as above 436432 Same as above Seas Sea - 385, 2305, 4225, 12545, 13185 ImpureSea - 65, 1985, 11105, 12385, 12575, 12705, 12865, 13025, 13215, 13345 TurquoiseSea 15, 255, 895, 95, 1695, 8375, 11135, 12735, 12895, 13055, 13375, 90015 SymmetricSea 255, 895, 11135, 13055 Patterns x0 - Sky x1 - ImpureLand, otherwise (Almost Pure) x2 - Land, otherwise Desert x3 - ImpureLand, otherwise (Contains Red) or (2 Layers of Greens) x4 - Land, otherwise (2 Layers of Greens) x5 - Underwater, otherwise Sea or TurquoiseSea x6 - ImpureLand, otherwise Beach x7 - ImpureLand, otherwise (Contains Red) x8 - Land, otherwise Desert x9 - ImpureLand, otherwise (Almost Pure) x01 - Valley x18 - Desert x32 - Desert x68 - Desert x82 - Desert y95 Turquoise Sea, otherwise Underwater 9..9- 2 Almost straight 5s at two sides x1111 ImpureLand with 4 Layers of 1s (Almost Pure) x applies to any integer, including 0 y applies to any 2's power z applies to any odd number, s applies to any even number Off Topic Stuff Some other patterns made with the same technique, which rather than being used for pattern-searching, these are just for fun. (And they have no patterns) http://prntscr.com/4naw53 (Nothing, purely trolling) http://prntscr.com/4nawky (Pi powers, rounded) http://prntscr.com/4navsa (Factorial) Category:Blog posts Category:Personal